A problem of Fekete
- 26 Downloads
The problem of whether an entire function f with nonnegative coefficients can be multiplied by another entire function g which “grows not faster” than f so that the product fg is a generating function of a Pólya frequency sequence of finite order (multipositive sequence in the sense of Fekete) is investigated.
KeywordsEntire Function Finite Order Frequency Sequence Nonnegative Coefficient
Unable to display preview. Download preview PDF.
- 1.S. Karlin, Total Positivity, Vol. 1, Stanford University Press, Stanford (1968).Google Scholar
- 2.M. Fekete and G. Pólya, “Über ein Problem von Laguerre,” Rend. Circ. Mat. Palermo,34, 89–120 (1912).Google Scholar
- 3.O. M. Katkova and I. V. Ostrovskii, “Null sets of entire generating functions of the Pólya frequency sequences of finite order,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 1, 13–15 (1988).Google Scholar
- 4.O. M. Katkova and I. V. Ostrovskii, “On null sets of entire generating functions of the Pólya frequency sequences of finite order,” Izv. Akad. Nauk SSSR, Ser. Mat.,53, No. 4, 771–781 (1989).Google Scholar
- 5.O. M. Katkova, “On indicators of entire functions of finite order with multipositive sequences of coefficients,” deposited at VINITI, Kharkov, No. 6 (1989).Google Scholar
- 6.O. M. Katkova, “On a method of construction of the Pólya frequency sequences,” Teor. Funkts. Anal. Ikh Prilozh., No. 51, 129–137 (1989).Google Scholar